# geo (finals)

a(4,3) b(7,4) and c(5,2) are midpoints of a triangle. find the coordinates for the vertices of the triangle!

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1. Let the vertices be A, B, and C, where A is the vertex opposite a(4,3) etc.

let's work on the x's first,
let the corresponding x's be p, q, and r

(p+q)/2 = 7
p + q = 14 -- #1
in the same way...
p + r = 10 -- #2
q + r = 8 -- #3

subtract #1 - #2
q - r = 4
2q = 12
q = 6
then r = 2
and p = 8

now do the y's the same way.

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posted by Reiny
2. wait what? I'm a bit confused here. so (4,3) would be on CB?

whats does corresponding x mean? and how did x appear?

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posted by SKipper
3. Yes, (4,3) is on CB
(5,2) on AB and (7,4) on AC

I let the points be A(p, ?), B(q, ?) and C(r, ?)

I then followed the definition of finding midpoints.
Don't you add up the x values , then divide by 2 , to get the x of the midpoint?

Pick your own values for the y's, and follow the same method.

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posted by Reiny
4. Sorry, but I got lost here...

I let the points be A(p, ?), B(q, ?) and C(r, ?)

^what does this?

I then followed the definition of finding midpoints.
Don't you add up the x values , then divide by 2 , to get the x of the midpoint?

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posted by SKipper

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